This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem e2

Description: A virtual deduction elimination rule. syl6 is e2 without virtual deductions. (Contributed by Alan Sare, 21-Apr-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e2.1	$⊢ (φ, ψ \to χ)$
	e2.2	$⊢ χ \to θ$
Assertion	e2	$⊢ (φ, ψ \to θ)$

Proof

Step	Hyp	Ref	Expression
1		e2.1	$⊢ (φ, ψ \to χ)$
2		e2.2	$⊢ χ \to θ$
3	1	dfvd2i	$⊢ φ \to (ψ \to χ)$
4	3 2	syl6	$⊢ φ \to (ψ \to θ)$
5	4	dfvd2ir	$⊢ (φ, ψ \to θ)$